## Manifold is a manifold with boundary?

Hi everyone,
I'm trying to show that an m-manifold is an m-manifold with boundary. I think that all I need to show is that any open set in R^m is diffeomorphic to an open set in the half plane H^m (={(x_1,...,x_m), x_m non-negative})

I can't seem to write down the diffeomorphism I need - I tried (x_1,...,x_m) |--> (x_1,...,x_m) if x_m non-negative, or (x_1,...,x_m-1,0) otherwise, but then it's doesn't have a well-defined inverse...

Any pointers?

Thanks.